31 citations · 256 across the 67 of their papers we have counts for
5 papers · 1 filter
Star chromatic index
Zdeněk Dvořák, Bojan Mohar, Robert Šámal
The star chromatic index of a graph is the minimum number of colors needed to properly color the edges of the graph so that no path or cycle of length four is bi-colo…
Spectrally degenerate graphs: Hereditary case
Zdenek Dvorak, Bojan Mohar
It is well known that the spectral radius of a tree whose maximum degree is D cannot exceed 2sqrt{D-1}. Similar upper bound holds for arbitrary planar graphs, whose spectral radius…
Three-coloring triangle-free graphs on surfaces I. Extending a coloring to a disk with one triangle
Zdenek Dvorak, Dan Kral, Robin Thomas
Let G be a plane graph with exactly one triangle T and all other cycles of length at least 5, and let C be a facial cycle of G of length at most six. We prove that a 3-coloring of…
Packing six T-joins in plane graphs
Zdenek Dvorak, Ken-ichi Kawarabayashi, Daniel Kral
Let G be a plane graph and T an even subset of its vertices. It has been conjectured that if all T-cuts of G have the same parity and the size of every T-cut is at least k, then G…
Sub-exponentially many 3-colorings of triangle-free planar graphs
Arash Asadi, Zdenek Dvorak, Luke Postle +1
Thomassen conjectured that every triangle-free planar graph on n vertices has exponentially many 3-colorings, and proved that it has at least 2^[n^(1/12)/20000] distinct 3-coloring…